Write 2014 with the first four prime numbers, with the
aid of the operations addition, multiplication and exponentiation.

Problems

Grades: 6th to 8th, 3rd to 5th

Expression/Equation

Algebraic Thinking

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.

Multiply and divide within 100.

3.OA.C.7, 4.OA.B.4, 6.EE.A.1

To the left, an 8 × 8
grid can be covered by one square (measuring 8 × 8), by four squares (measuring
4 × 4 each), or by ten squares (one 5 × 5, three 3 × 3,
two 2 × 2, and four 1 × 1).

Find all values of *n* for which it is impossible to cover an
8 × 8 grid with *n* squares of
integer side length.

Problems

Grades: 3rd to 5th

Measurement & Data

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

3.MD.C.5a, 3.MD.C.5b, 3.MD.C.6

Consider
three six-sided dice A, B, and C, with the following numbers on their sides:

A: 2, 2, 4, 4, 9, 9

B: 1, 1, 6, 6, 8, 8

C: 3, 3, 5, 5, 7, 7

What
is the probability that:

· A produces a higher number than B?

· B produces a higher number than C?

· C produces a higher number than A?

Can
you find another set of face values for A, B, and C that yield the same
properties? (Does such a set even exist?)

Problems

Grades: 6th to 8th

Stats & Probability

Investigate chance processes and develop, use, and evaluate probability models.

7.SP.C.5, 7.SP.C.7a

A 40‑inch straightedge
(without markings) is divided into four pieces. The length of each piece is an
integer number of inches. These four pieces, when used in tandem, can be used
to measure any integer length from 1 to 40 inches.

What are the lengths of the
pieces?

Problems

The rectangle shown consists of eight squares. The length of each side of each
square is 1 unit. The length of the shortest path from A to C using the lines
shown is 6 units.

How
many different six-unit paths are there from A to C?

Problems